Informal proof, formal proof, formalism

Weir, A. (2016) Informal proof, formal proof, formalism. Review of Symbolic Logic, 9(1), pp. 23-43. (doi: 10.1017/S1755020315000234)

Abstract

Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur. In this paper I look at the relevance of these issues for formalism, construed as an anti-platonistic metaphysical doctrine. I argue that there are strong reasons to doubt that all proofs are fully formalisable, if formal proofs are required to be finitary, but that, on a proper view of the way in which formal proofs idealise actual practice, this restriction is unjustified and formalism is not threatened.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Weir, Professor Alan
• Authors: Weir, A.
• College/School: College of Arts & Humanities > School of Humanities > Philosophy
• Journal Name: Review of Symbolic Logic
• Publisher: Cambridge University Press
• ISSN: 1755-0203
• ISSN (Online): 1755-0211
• Published Online: 07 August 2015
• Copyright Holders: Copyright © 2015 Cambridge University Press
• First Published: First published in Review of Symbolic Logic 9(1):23-43
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.